A known conventional steering assist device to assist the steering of a vehicle is one disclosed in Japanese Patent Application Laid-Open No. 2001-10518, where a view ahead of the vehicle is captured by a camera, positions of a traveling path and a vehicle with respect to the traveling path are detected based on the captured image information, a basic steering assist torque is computed based on the shape of the traveling path, a corrected steering assist torque is computed based on the position of the vehicle, an output steering assist torque is computed based on the basic steering assist torque and the corrected steering assist torque, and the control input of the steering actuator is determined based on the output steering assist torque. This device attempts to improve control accuracy by controlling the steering using a shape parameter of the traveling path and position parameter of the vehicle, which are detected at high accuracy, without using a yaw rate.